Rodrigo, Marianito R.2021-08-272021-08-272021-06-26Rodrigo, M. R. (2021). An elementary method for obtaining general solutions to systems of ordinary differential equations. <i>Electronic Journal of Differential Equations, 2021</i>(58), pp. 1-20.1072-6691https://hdl.handle.net/10877/14468An analytical method is proposed for finding the general solution of a system of ordinary differential equations (ODEs). The general solution is expressed as a series which in some cases can be summed to give an expression in closed form. A sufficient condition for the series to converge is derived. Illustrative examples are given for scalar first-order ODEs (Riccati, Abel, homogeneous, Bernoulli, linear, separable) and for higher order ODEs (Airy, linear oscillator, Lienard, van der Pol). The method relies only on a calculus background.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalOrdinary differential equationGeneral solutionAnalytical methodExact solutionArticle